{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "446b335a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12 1.414213562373095\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x = 2\n",
    "def calXnew(Xold):\n",
    "    return (x-1) / Xold + Xold / x\n",
    "Xold = 100\n",
    "Xnew = 0\n",
    "i = 1\n",
    "difference = 1\n",
    "\n",
    "listXNEW = []\n",
    "list_i = []\n",
    "listDiff = []\n",
    "\n",
    "while difference > 0.0000001:\n",
    "    Xnew = calXnew(Xold)\n",
    "    listXNEW.append(Xnew)\n",
    "    list_i.append(i)\n",
    "    difference = abs(Xnew - Xold)\n",
    "    listDiff.append(difference)\n",
    "    Xold = Xnew\n",
    "    i += 1\n",
    "\n",
    "print(i, Xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0383f454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9f317a61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[50.01,\n",
       " 25.024996000799838,\n",
       " 12.552458046745903,\n",
       " 6.35589469493114,\n",
       " 3.335281609280434,\n",
       " 1.967465562231149,\n",
       " 1.4920008896897232,\n",
       " 1.4162413320389438,\n",
       " 1.4142150140500531,\n",
       " 1.41421356237384,\n",
       " 1.414213562373095]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "listXNEW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2007011b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e49b65d220>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list_i,listXNEW)\n",
    "y=[1.414213]*len(list_i)\n",
    "plt.plot(list_i,y)\n",
    "plt.xlabel(\"iteration number\",fontsize = 18)\n",
    "plt.ylabel(\"Xnew\",fontsize = 18)\n",
    "plt.legend([\"Iteration\",\"y=1.414\"],fontsize = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "034f44fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14 1.414213562373095\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x = 2\n",
    "def calXnew(Xold):\n",
    "    return (x-1) / Xold + Xold / x\n",
    "Xold = 400\n",
    "Xnew = 0\n",
    "i = 1\n",
    "difference = 1\n",
    "\n",
    "listXNEW = []\n",
    "list_i = []\n",
    "listDiff = []\n",
    "\n",
    "while difference > 0.0000001:\n",
    "    Xnew = calXnew(Xold)\n",
    "    listXNEW.append(Xnew)\n",
    "    list_i.append(i)\n",
    "    difference = abs(Xnew - Xold)\n",
    "    listDiff.append(difference)\n",
    "    Xold = Xnew\n",
    "    i += 1\n",
    "print(i, Xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0911e85d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e49b79a7f0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list_i,listXNEW)\n",
    "y=[1.414213]*len(list_i)\n",
    "plt.plot(list_i,y)\n",
    "plt.xlabel(\"iteration number\",fontsize = 18)\n",
    "plt.ylabel(\"Xnew\",fontsize = 18)\n",
    "plt.legend([\"Iteration\",\"y=1.414\"],fontsize = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "900774b9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
